Kutz, Jose NBrunton, Steven LClark, Emily Elizabeth2020-10-262020-10-262020-10-262020Clark_washington_0250E_22009.pdfhttp://hdl.handle.net/1773/46548Thesis (Ph.D.)--University of Washington, 2020In this era of big data, many systems of interest to researchers are too large to fully sample. Thus, significant downsampling is necessary, but determining the best locations for optimal full-state reconstructions is an NP-hard problem. Solving for the optimal sensor selections would require the researcher to test all ${n \choose p}$ combinations of placing $p$ sensors given $n$ possible locations, which is only feasible for very small systems. Instead, researchers have developed techniques to calculate near-optimal sensor placements, usually based on convex relaxations or greedy algorithms. This text focuses on a well-known greedy algorithm, the column-pivoted QR decomposition, which is performed on basis modes from a low-rank decomposition of the system, to pick out sensor locations that are approximately maximally informative and robust to noise. The column-pivoted QR decomposition is efficient and has proven optimality guarantees, but it does not account for several important practical considerations, including sensor cost, purpose, and type. In this work, we extend the QR decomposition to account for some of these real-world constraints. First, we modify the algorithm to account for a heterogeneous cost function on sensor location, selecting sensors that are approximately Pareto optimal in cost and reconstruction quality. Next, we demonstrate that the cost-constrained column-pivoted QR decomposition can be applied to modal bases beyond the most common basis of singular vectors. In this way, we can select sensors and actuators for control systems, account for a system's estimated equations of motion, and even select sensors without training data. Finally, we approach the problem of multi-fidelity sensor selection, that is, determining where and how many of each type of sensor to place, given a fixed budget and access to cheap, high-noise sensors and expensive, low-noise sensors. This problem is complex and has a very large parameter space, but we develop guidelines for asymptotic cases of sensor cost and noise level. The above methods are demonstrated on examples from physics, climate science, and facial recognition, showing that it is possible to improve sensor effectiveness and decrease cost by considering real-world practicalities.application/pdfen-USCC BYControl theoryGreedy algorithmsReduced order modelingSensorsPhysicsApplied mathematicsMechanical engineeringPhysicsThesis